Stat 351 Homework #2
Due date: Tuesday, June 23, 2020 at 11.59 p.m. CDT.
Submit your homework via one of the following methods.
1. Type your answers in a word document and submit as a word document file or pdf file.
2. Write down your answers in separate sheets of paper and submit the scan copy of the answer.
3. Write down your answers in separate sheets of paper and submit snapshot of the answer.
Make sure to show your work for full credit.
Questions 1 and 2 are based on Sections XXXXXXXXXXModel assumption and testing.
1. A Regression analysis was applied between sales data (y in $1000s) and advertising
expenditure (x in $100s) and the estimated regression equation is obtained as
yÌ‚ = XXXXXXXXXX8x.
Suppose SST = 300, SSE = 75, sb1 = XXXXXXXXXXand ? = 17
a) Ca
y out a t-test to see whether the advertising expenditure is significant. Use
Î± = 0.05 and critical value approach to draw your conclusion. Make sure to
show all your steps.
) Ca
y out an F-test to see whether the advertising expenditure is significant.
Use Î± = 0.05 and critical value approach to draw your conclusion. Make sure
to show all your steps.
2. A sales manager collected data on annual sales for new customer accounts and the
number of years of experience for a sample of 15 salespersons. The following is
the Regression Analysis run by Minitab for developing an estimated regression
equation to predict annual sales using the independent variable years of experience
(x). Note that ? = ????? ?? ??????????, ? = ?????? ?????.
Regression Analysis: Annual Sales versus Years of Experience
Regression Equation
Annual Sales = XXXXXXXXXXYears of Experience
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant XXXXXXXXXX000
Years of
Experience
XXXXXXXXXX XXXXXXXXXX
Model Summary
S R-sq R-sq(adj) R-sq(pred)
XXXXXXXXXX% 95.89% 95.17%
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression XXXXXXXXXX XXXXXXXXXX
Years of Experience XXXXXXXXXX XXXXXXXXXX
E
or XXXXXXXXXX
Lack-of-Fit XXXXXXXXXX0.901
Pure E
or XXXXXXXXXX
Total XXXXXXXXXX
Settings
Variable Setting
Years of Experience 9
Prediction
Fit SE Fit 95% CI 95% PI
XXXXXXXXXX.095, XXXXXXXXXX, XXXXXXXXXX)
a) Ca
y out a t-test to see whether the years of experience and the annual sales are
elated. Use Î± = 0.05. Please use the P-value approach to answer this question.
) Ca
y out an F-test to see whether years of experience and the annual sales are
elated. Use Î± = 0.05. Please use the P-value approach to answer this question.
c) Find a 95% confidence interval for the mean annual sales for all salespersons
with nine years of experience.
d) The company is considering hiring Tom Smart, a salesperson with nine years of
experience. Find a 95% prediction interval of annual sales for Tom Smart.
e) Discuss the differences in your answers to part c) and d). That is, which interval
estimation is wider? And why?
Questions 3 is based on Sections XXXXXXXXXXResidual analysis.
3. The following data were used to develop a regression analysis.
x XXXXXXXXXX
y XXXXXXXXXX
a) The graph shown below is the residual against the fitted value (ï¿½Ì‚ï¿½) to check
the constant variance assumption.
Does the above plot support the assumptions about the e
or ?? Explain.
) The graph shown below is the normal probability to check the normality
assumptions about the e
or ?.
Does the above plot support the assumptions about the e
or ?? Explain.
c. The following results are part of the Regression Analysis for the above data
from Minitab. Below is a table with statistics necessary for analyzing the
esiduals.
SRES stands for standardized residual and HI for leverage values.
Table 1: Residual Analysis
Observation
SRES HI
1
XXXXXXXXXX
2
XXXXXXXXXX
3
XXXXXXXXXX
4
XXXXXXXXXX
5
XXXXXXXXXX
6
XXXXXXXXXX
7
XXXXXXXXXX
8
XXXXXXXXXX
9
XXXXXXXXXX
I. Can any of the observations be classified as an outlier?
II. Can any of the observations be classified as an influential
observation?
Questions 4 is based on Sections from chapter 15.
4. This question is from the textbook: Problem 25 on Page 705.
The Minitab output for this question is given below.
Regression Analysis: Overall versus Itineraries/Schedule, Shore Excursions,
Food/Dining
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant XXXXXXXXXX016
Itineraries/Schedule XXXXXXXXXX XXXXXXXXXX
Shore Excursions XXXXXXXXXX XXXXXXXXXX
Food/Dining XXXXXXXXXX XXXXXXXXXX
Model Summary
S R-sq R-sq(adj) R-sq(pred)
XXXXXXXXXX% 70.29% 58.09%
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression XXXXXXXXXX XXXXXXXXXX
Itineraries/Schedule XXXXXXXXXX0.407
Shore Excursions XXXXXXXXXX XXXXXXXXXX
Food/Dining XXXXXXXXXX XXXXXXXXXX
E
or XXXXXXXXXX
Total XXXXXXXXXX
Prediction for Overall
Settings
Variable Setting
Itineraries/Schedule 90
Shore Excursions 80
Food/Dining 88
Prediction
Fit SE Fit 95% CI 95% PI
XXXXXXXXXX.6283, XXXXXXXXXX, XXXXXXXXXX)
Please answer ONLY for parts of a, b, c (Do not answer for part d) and the following
part e and f.
e. Provide a 95% confidence interval for the mean value for all ships that got
Itineraries/Schedule score 90, Shore Excursions score 80 and Rood/Dining score 88.
f. Provide a 95% prediction interval for the mean value for one specific ship that got
Itineraries/Schedule score 90, Shore Excursions score 80 and Rood/Dining score 88.